Composed of perfluorinated backbone with sulfonate sidechains, Nafion self-assembles upon hydration and segregates into interpenetrating hydrophilic and hydrophobic subphases. This segregated morphology determines the transport properties of Nafion membranes that are widely used as compartment separators in fuel cells and other electro-chemical devices, as well as permselective diffusion barriers in protective fabrics. We introduce a coarse-grained model of Nafion, which accounts explicitly for polymer rigidity and electrostatic interactions between anionic sidechains and hydrated metal cations. By means of dissipative particle dynamics (DPD) and Monte Carlo (MC) simulations, we explore geometrical, transport, and sorption properties of hydrated Nafion-type polyelectrolyte membranes. Novel methodology will be presented for calculating water adsorption isotherms and transport coefficients as a function of the degree of hydration.